The analysis shows that the Lax-Wendroff method is based on non-uniform compact schemes for non-uniform grids can be employed for DNS with much reduced grid requirement than for central difference methods for two reasons. First, the method provides a higher value of \((kh)_{max}\)  and hence one would require lesser number of points per wave (PPW). Secondly, the usage of non-uniform grid will allow one to appropriately refine the mesh where needed, coupled with the judicious choice of stretching factor of the mesh. We have already provided details on the resolution requirements and constraints for DNS, LES simulations for the Lax-Wendroff method used along with NUC6. Next, we evaluate the property charts for the case of Lax-Wendroff method that is developed for a non-uniform compact scheme, i.e. applied on a uniform grid as a special case, so that we can compare the two and also check for the consistency of the methods. In this limit, NUC6 scheme reduces to the well-known Lele's sixth order compact scheme [1]}.
